How can I serialize internal classes using XmlSerializer?

I'm building a library to interface with a third party. Communication is through XML and HTTP Posts. That's working.

But, whatever code uses the library does not need to be aware of the internal classes. My internal objects are serialized to XML using this method:

internal static string SerializeXML(Object obj)
{
    XmlSerializer serializer = new XmlSerializer(obj.GetType(), "some.domain");

    //settings
    XmlWriterSettings settings = new XmlWriterSettings();
    settings.Indent = true;
    settings.OmitXmlDeclaration = true;

    using (StringWriter stream = new StringWriter())
    {
        using (XmlWriter writer = XmlWriter.Create(stream, settings))
        {
            serializer.Serialize(writer, obj);
        }
        return stream.ToString();
    }
}

However, when I change my classes' access modifier to internal, I get an exception at runtime:

[System.InvalidOperationException] = {"MyNamespace.MyClass is inaccessible due to its protection level. Only public types can be processed."}

That exception happens in the first line of the code above.

I would like my library's classes not to be public because I do not want to expose them. Can I do that? How can I make internal types serializable, using my generic serializer? What am I doing wrong?